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Prepare a grill or grill pan for medium-high heat cooking.
Meanwhile, combine sugar, thyme leaves and 1/4 cup water in a small saucepan.
Set over high heat and bring just to a boil, stirring to dissolve sugar.
Let cool to room temperature.
Grill nectarines, flipping halfway through, until charred in parts and soft and juicy, 8 to 10 minutes total.
Let cool, then transfer to a large bowl.
Using a wooden spoon, mash nectarines until very juicy and pulpy.
Add thyme syrup and about 1 cup of the wine and stir well, continuing to muddle solids until completely mashed.
Strain mixture through a fine-mesh strainer into a large pitcher, pressing to extract as much liquid and nectarine pulp as possible; discard solids.
Pour remaining wine into the pitcher and stir to combine.
Fill 4 to 6 glasses with ice and pour in nectarine punch.
Garnish with thyme sprigs and nectarine slices.